Credit card payoff calculator

How does a credit card payoff calculator work?

A card balance shrinks only by the part of each payment left over after that month's interest. The calculator charges interest every month at the APR divided by 12 on the balance you carry into the month, adds it, then takes off your payment. It repeats that until the balance reaches zero and counts the months and the interest along the way. It assumes no new spending on the card, no fees and one APR throughout.

With the defaults, a $5,000 balance at 22% APR paid at $200 a month clears in 34 payments, or 2 years 10 months. You pay $6,749.88 in total, of which $1,749.88 is interest. The first month's interest is $91.67, so only $108.33 of the first $200 comes off the balance. The Clear it by a month tab works the other way round: you choose the number of months and it finds the level payment, which is $259.39 a month for 24 months on the same card.

How do you calculate credit card payoff time by hand?

For a fixed payment P on a balance B with monthly rate i, the number of months is n = -ln(1 - B x i / P) / ln(1 + i). Using the default card:

1. Monthly rate: i = 22% / 12 = 1.8333% = 0.0183333.
2. Interest share of the payment: B x i / P = 5,000 x 0.0183333 / 200 = 0.458333. The first month's interest takes 45.8% of the payment.
3. Top line: -ln(1 - 0.458333) = -ln(0.541667) = 0.613104.
4. Divide: 0.613104 / ln(1.0183333) = 0.613104 / 0.018167 = 33.75 months.

A fraction of a month means one extra, smaller payment: 33 full payments of $200 and a 34th of $149.88. If B x i / P is 1 or more, the logarithm has no answer, which is the formula's way of saying the payment never clears the balance. In year 1 alone the default card is charged $960.57 of interest, and after 12 payments $3,560.57 is still owed.

How long does it take to pay off a credit card with minimum payments?

A card agreement can set the minimum as a percentage of the balance with a fixed floor; here the percentage is taken from the balance after that month's interest is added. Because the percentage is taken from a falling balance, the minimum falls too, and the debt shrinks more slowly each month. Turn on the minimum-payment plan, enter the percentage and the floor from your card agreement, and the calculator runs that plan beside yours. On the $5,000 card at 22% APR:

The 1% rule never clears this card because 1% of the balance is less than the 1.83% of interest added each month; the balance would fall only once it dropped low enough for the $25 floor to take over, and from $5,000 it never gets there. The fixed $200 plan saves $4,968.43 of interest against the 3% minimum. The percentage and floor here are examples to show the arithmetic, not any lender's terms.

What payment pays off a credit card by a set date?

Choose the Clear it by a month tab and enter how many months you want the card to take. The payment is the level amount that brings the balance to zero in exactly that many months: P = B x i x (1 + i)^n / ((1 + i)^n - 1), or simply B / n at 0% APR. For the $5,000 card at 22%:

Doubling the time from 12 to 24 months cuts the payment by $208.58 but roughly doubles the interest. To turn a target date into months, count the payments between now and that date; a payment due this month counts as month 1.

Worked examples in three currencies

The arithmetic is the same in every currency, and nothing is converted. The APRs below are chosen for illustration and are not any card's rate.

The £3,000 card on a minimum of 3% with a £25 floor would start at £91.87 a month and take 15 years 7 months, with £5,151.06 of interest. In the dirham example, interest is more than half the original balance even though the payment is 5% of it, because 36% APR adds 3% a month. Pick a currency in the selector and untouched defaults are resized to round amounts for it; anything you have typed stays as typed.

How do the payment and the APR change the payoff time?

The payment matters most, because every extra unit goes straight to the balance. On the $5,000 card at 22%:

A higher APR stretches the same payment further. At $200 a month the card clears in 31 months with $1,032.66 of interest at 15% APR, in 34 months with $1,749.88 at 22%, and in 39 months with $2,762.43 at 29%. The payment also has a floor below which nothing works: it has to exceed the first month's interest, $91.67 here. At $90 a month the balance grows instead, to $5,179.49 after five years, and the calculator says so in place of a payoff date.

What does the minimum payment warning on a US card statement show?

In the United States, Regulation Z, 12 CFR 1026.7(b)(12), as published by the CFPB, sets the repayment disclosures on credit card statements. Under it, the statement carries a box headed Minimum Payment Warning that shows:

• how long the balance on that statement would take to repay making only minimum payments, and the estimated total cost;
• a statement that both estimates assume only minimum payments and nothing else added to the balance;
• unless an exemption applies, the monthly payment that would repay the balance in 36 months, its total cost and the saving against minimum payments;
• a toll-free number for credit counseling information.

When the minimum payment would not cover the interest, a different warning is used. The 36-month figures are left out, for example, when minimum payments would already clear the balance in 3 years or less. The CFPB's consumer guidance on this box says you are required to pay only the minimum, and that the 36-month figure is based on the current balance without future purchases. This calculator's Payment to clear in 36 months tile works out the same kind of figure from the APR you enter, but an issuer's own estimate uses its own minimum formula and terms, so the two can differ. Card rules in other countries are not modeled here.

How do you calculate credit card payoff in Excel?

Two Excel functions cover both tabs. Microsoft documents NPER(rate, pmt, pv, [fv], [type]), which returns the number of periods, and PMT(rate, nper, pv, [fv], [type]), which returns the payment; for monthly payments the rate is the annual rate divided by 12.

• Months to clear: =NPER(22%/12, -200, 5000) returns 33.75, which rounds up to 34 payments, matching the calculator.
• Payment to clear in 24 months: =PMT(22%/12, 24, -5000) returns 259.39.
• Interest: for the PMT case, multiply the unrounded payment by the months and subtract the balance: 259.3908 x 24 - 5,000 = 1,225.38. Using the rounded 259.39 gives 1,225.36.

The balance and the payment take opposite signs: money you receive (the balance) is positive and money you pay out is negative. Leave type out, or set it to 0, so payments fall at the end of each month, which matches this calculator. NPER cannot show a minimum-payment plan, because that payment changes every month; for that you need a row-by-row schedule like the one under the calculator.

Common mistakes and what this calculator leaves out

• Treating the minimum as a plan. It is the least the card accepts this month, and it shrinks as the balance shrinks.
• Spending on the card while paying it down. New purchases add to the balance; the payoff time here assumes none.
• Ignoring promotional rates ending. An introductory rate that rises later changes every figure after that month.
• Comparing payments, not interest. A smaller payment looks easier and almost always costs more in total.

The calculator uses one APR for the whole balance, interest at APR / 12 each month, the payment taken at the end of each month and no fees. A balance below half the currency's smallest unit, half a cent in dollars, counts as cleared. Card agreements can compute interest daily on an average daily balance and apply different APRs to purchases, cash advances and balance transfers, so a statement figure can differ slightly. It does not model late fees, annual fees, penalty rates or balance transfers, and it stops counting at 100 years.

Glossary

APR: the annual percentage rate on the card; here the monthly rate is APR / 12. Balance: what you owe after the latest payment. Minimum payment: the least the card accepts in a month, set by the card agreement. Floor: the fixed amount a minimum payment never goes below while the balance is larger. Payoff schedule: each payment split into interest and the amount that reduces the balance. Negative amortization: a balance that grows because the payment does not cover the interest. Regulation Z: the US federal rule, published by the CFPB, that sets credit card statement disclosures.

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